Normal distribution was invented by ________.

(a)

Laplace

(b)

De-Moivre

(c)

Gauss

(d)

all the above

If X ~ N(9,81) the standard normal variate Z will be ________.

(a)

\(Z=\frac { X- 81 }{ 9 } \)

(b)

\(Z=\frac { X-9 }{ 81 } \)

(c)

\(Z=\frac { X-9 }{ 9 } \)

(d)

\(Z=\frac { 9-X }{ 9 } \)

 In turning out certain toys in a manufacturing company, the average number of defectives is 1%. The probability that the sample of 100 toys there will be 3 defectives is ________.

(a)

0.0613

(b)

0.613

(c)

0.00613

(d)

0.3913

The parameters of the normal distribution \(f(x)=\left(\frac{1}{\sqrt{72 \pi}}\right)\)\(\frac{e^{-(x-10)^{2}}}{72}\) –∞ <  x  <  ∞ ________.

(a)

(10,6)

(b)

(10,36)

(c)

(6,10)

(d)

(36,10)

A manufacturer produces switches and experiences that 2 per cent switches are defective. The probability that in a box of 50 switches, there are atmost two defective is ________.

(a)

2.5 e^-1

(b)

e^-1

(c)

2e^-1

(d)

none of the above

An experiment succeeds twice as often as it fails. The chance that in the next six trials, there shall be at least four successes is ________.

(a)

240/729

(b)

489/729

(c)

496/729

(d)

251/729

If for a binomial distribution b(n,p) mean = 4 and variance = 4/3, the probability, P(X ≥ 5) is equal to ________.

(a)

(2/3)⁶

(b)

(2/3)⁵(1/3)

(c)

(1/3)⁶

(d)

4(2/3)⁶

The average percentage of failure in a certain examination is 40. The probability that out of a group of 6 candidates atleast 4 passed in the examination are ________.

(a)

0.5443

(b)

0.4543

(c)

0.5543

(d)

0.4573

Forty percent of the passengers who fly on a certain route do not check in any luggage. The planes on this route seat 15 passengers. For a full flight, what is the mean of the number of passengers who do not check in any luggage?

(a)

6.00

(b)

6.45

(c)

7.20

(d)

7.50

Which of the following statements is/are true regarding the normal distribution curve?

(a)

it is symmetrical and bell shaped curve

(b)

it is asymptotic in that each end approaches the horizontal axis but never reaches it

(c)

its mean, median and mode are located at the same point

(d)

all of the above statements are true.